SOLUTION: What is the 10th term of the sequence 64, 16, 4,...? a. 1/2024 b. 1/256 c. 1/4096 d. 1/496

Question 853272: What is the 10th term of the sequence 64, 16, 4,...?
a. 1/2024
b. 1/256
c. 1/4096
d. 1/496
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
Find the type of sequence. This is a geometric sequence with a common term of 1/4, because each term * 1/4 is the next term.

For any geometric sequence, the nth term = where a(1) is the first term, n is the term number you're trying to find, and r is the common ratio.

Let's test it with the third term. The third term = = 64/16 = 4. That is the third term. See, it works!

The tenth term is = 64/262144 = 1/4096. The answer is c.

If you didn't remember the formula, write out the terms, dividing each subsequent term by 4 (which is multiplying it by 1/4), until you reach the 10th term.

64, 64/4=16, 16/4=4, 4/4=1, 1/4=1/4, 1/4 / 4 = 1/16, 1/16 / 4 = 1/64, 1/64 / 4 = 1/256, 1/256/4 = 1/1024, 1/1024 / 4 = 1/4096.

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